On Path 1, we get the boss of the Meteor, the Dancing Insector. It starts out invincible, but shooting its legs enough would knock it on the floor, damaging the shield. After doing so twice, the shield is destroyed, allowing the legs to be destroyed themselves. While dodging the plasma balls and it charging at you, the legs fall off one by one. After they're all gone, the main body goes on a last stand. Firing fire at you and hopelessly charging until it is destroyed.
Later on Path 1, we get Phantron. It flies back and forth at lightning fast speeds in Venom's orbit, and you need to fly left and right to keep shooting Phantron. After taking down enough of its health, it creates illusions of itself that fire real shots. From here on out, it's a matter of finding Phantron and defeating it. It only retreats, however, and shows up later on the actual planet itself. There, Phantron immediately clones itself, and the same process as phase 2 of the first fight must be performed. When its health is almost gone, though, it goes One-Winged Angel and gains legs. Phantron is now a much harder target and requires a skilled player to defeat it, firing all over the place, jumping, and creating more illusions. Defeating Phantron here will finally finish it off for good, allowing one to face Big Bad Andross.
Path 2 features what is perhaps the easiest boss in the game, Professor Hangar, on Titania. However, just because the boss is easy doesn't mean it's not fun. Hangar is a coward, starting the fight off by forcing you to fight against certain enemies. After defeating them, Hangar shows itself and fights, firing enemies at you and using Shadow Thrusters to fire clones at you. After using the Shadow Thrusters, the cycle repeats, with regular enemies attacking while Hangar heals.
Immediately after Hangar, you go to Sector Y, which features Plasma Hydra as the boss. It is actually a rather difficult boss, but still a fun one. You have to shoot its hands enough to destroy the arms, which will damage Plasma Hydra, though it will immediately regrow its arms. While this happens, Plasma Hydra will fire plasma balls at you and spin around in order to make its arms hit you. After destroying enough arms, Plasma Hydra will get rid of the arms and grow a giant tongue, at which point the main body is vulnerable. After finally putting Plasma Hydra down, it trys to ram into you as a Kaizo Trap and, afterwards, rapidly somersault backwards in space, where it finally explodes, letting you move onto Venom.
In Path 3, Monarch Dodora is ready to greet you at the end of Fortuna. Unlike the other bosses, Monarch Dodora is a living, rational creature and fights like one, preferring to run into you, jump, lay eggs to create babies to attack you, and breathing fire. Monarch Dodora's body is its weak point, but it is completely invulnerable. To make it vulnerable, either the tail or both heads must be shot in so that the end of the tail or the heads are touching the body. Afterwards, the body will start flashing and will become vulnerable to attack, at which point you must shoot the body as much as possible to defeat Monarch Dodora.
If you want to go to Venom on Path 3, the Spinning Core on Macbeth will try and stop you. The Spinning Core will come right out of the ground when approached and fire a shot before you can reasonably target it. After you get close enough, its turrets will be in full view, allowing you to shoot them down while the Core fires at you. After destroying half of them, the Core will open up and start firing four missiles at a time at you, in addition to the earlier shots. After destroying them all, the Spinning Core jumps into the air and comes back upside down, revealing its true weakpoint, though it's defended by four blue orbs that will change distances from the weakpoint to damage you when you're close. When it retreats, however, the Core will wildly fire at you as a last stand and it becomes a nerve-wracking battle to see who can defeat the other first. After destroying the weakpoint, the Spinning Core's main body falls to the ground and explodes.
The Great Commander. Not the universally reviled Orbit fight, but the ground fight, where the Great Commander reveals that it recovered from the Orbit fight and transforms into a giant ROB lookalike. Here, the Great Commander fires out of a small turret on the bottom ship which is also its weakpoint. While firing, the Great Commander can also start firing energy rings at you or throw iron balls. After destroying the bottom ship, the other ships start flying seperately, with the middle ship rapidly spinning at you and the upper ship firing at you, including dropping a weird missile that bounces off of the ground. The upper ship is completely vulnerable and must be destroyed to end the battle. Afterwards, the middle ship, the only one left, loses all battle capacity and crashes, finally ending the existence of the Great Commander and granting access to Andross.
The Slot Machine in Out of this Dimension is not an awesome boss because of the fight itself, or because it's a final boss. It's awesome because it's a perfect boss for the utter Mind Screw the level is. After shooting down a giant asteroid, flying into a giant bird from an egg inside the asteroid, surviving assaults from airplanes, and watching the horribly distorted background while listening to ballet music, a Japanese children's song starts playing as a huge Slot Machine flies in. The fight is all about luck - how fast you can get Triple 7s before the remix of the aforementioned Japanese children's song, When the Saints Go Marching In, and Lightly Row get to your head, while dodging the random attacks the Androsses give you and collecting the healing money the Cherries get you. After finally getting the Triple 7s, the Slot Machine basically fully heals you and explodes, allowing you to play through the Mind Screw Gainax Ending. It's VERY fitting for the level and a very memorable final boss.
Any appearance of the Star Wolf team in Star Fox 64. Special note to their appearance on Bolse, because Bolse is pure awesomeness all by itself. (And is nominated as such here, since the satellite is the boss—and fights back with FRIKKIN LASER BEAMS once you start to take out its core).
There's nothing quite like skipping through their intro cutscenes (especially on Fichina) and shooting them down before they even break formation.
Also, the train conductor on Macbeth, who taunts you all throughout the level. His Mechbeth can become That One Boss, but this can be averted by sending the train crashing into the weapons factory, which is the most satisfying feeling ever and still probably the #1 moment in controller rumbling history. (And yes, the William Shakespeare reference was absolutely necessary—supplementary material says that Andross tore down a Birnam Wood to build that weapons factory there.)
"I can't STOP IT!!!"
Speaking of which, Andross himself made for some memorable boss battles. Be it the face in the original or the giant brain with detachable eyeballs in Star Fox 64.
Drakor from Star Fox Adventures is an absolute blast to fight. It resembles a first-person rail shooter, in stark and abrupt contrast to the third-person Zelda-esque adventuring that you've been doing the whole time up to this point, but the whole fight is really quite fun and it leaves you with a great feeling of exhiliration and satisfaction after it's done.
Drakor's fine but the finest hour of Star Fox Adventures will always be the battle against the Red-Eyes King. A truly enormous, building-sized T-Rex hunting in the enclosed labyrinth of a sacred temple? Fuck yes. Plus the creature is so massive it is completely immune to ALL of Fox's attacks, requiring you to trick it into stepping into an electrode trap and then throw a bomb at it. And it's tough enough to survive multiple bombs to the face. Bringing this beastie down will truly make you feel like a Badass.
The final battle against the Aparoid Queen from Star Fox: Assault is definitely one of the best fights in the series.
For the first phase, you have an all-range mode battle against a moth-like insectoid. She can summon larval Aparoids to aid her, and can unleash a massively powerful attack that covers almost half the arena, while you're blasting away at the armor covering her abdomen, where her weak spot is. Eventually, you defeat her, and launch the self-destruct program into her body, causing her entire upper portion to explode off. The fight seems finished, only for the remaining stump to begin retracting deeper into the planet, still talking. Fox and his crew fly after her, for the final battle.
At this point the fight moves to its second phase, an on-rails portion descending into the Aparoid planet. The damaged stump rotates around, revealing that it was just a small part of the true Aparoid Queen, a massive behemoth with four large mouthes and four large orbs. As you dodge its projectiles and shoot at the orbs, the center eventually opens up, revealing a massive dragon-like head that serves as its weak point and its most powerfulweapon. At this point, your allies actually prove useful, with one of them (possibly even Slippy) flying in to join you in shooting at the boss's head, while you cover him/her from the massive minefield the Aparoid Queen deploys.
After you deplete all her health again, however, the final phase begins, with most of the Queen's body blowing up to reveal a relatively simple, twitchy bug-like entity. Your allies back off to let you fight it one-on-one, in an awesome gimmick-free shoot-out, with it launching ludicrously powerful beam attacks at you while you shoot at its face as fast as you can to finish it off once and for all. The music, both for the all-range and on-rails portions, is really incredible, too. And it's surprisingly challenging on Hard Mode.